x/12x+7-11=5x-840

Solution for x/12x+7-11=5x-840 equation:

x/12x+7-11=5x-840

We move all terms to the left:

x/12x+7-11-(5x-840)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

x/12x-(5x-840)-4=0

We get rid of parentheses

x/12x-5x+840-4=0

We multiply all the terms by the denominator


x-5x*12x+840*12x-4*12x=0

Wy multiply elements

-60x^2+x+10080x-48x=0

We add all the numbers together, and all the variables

-60x^2+10033x=0

a = -60; b = 10033; c = 0;
Δ = b2-4ac
Δ = 100332-4·(-60)·0
Δ = 100661089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100661089}=10033$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10033)-10033}{2*-60}=\frac{-20066}{-120}
=167+13/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10033)+10033}{2*-60}=\frac{0}{-120}
=0
$